A first measurement of the ΛΛ and ΛΛ (ΛΛ) spin compositions in hadronic Z0 decays

19 September 1996

PHYSICS LETTERS B

EISEVDER Physics Letters B 384 (1996) 377-387

A first measurement of the A& and RR (&A) spin compositions in hadronic 2’ decays

OPAL Collaboration

G. Alexander w, J. Allisonr, N. Altekamp e, K. Ametewee y, K.J. Anderson’, S. Anderson[, S. Arcelli b, S. Asai x, D. Axen ac, G. Azuelos r~l, A.H. Ball 4, E. Barberio Z, R.J. Barlow P,

R. Bartoldus ‘, J.R. Batley e, G. Beaudoin’, J. Bechtluft n, C. Beestoni’, T. Behnke h, A.N. Bell a, K-W. Bell t, G. Bella”, S. Bentvelsen h, P. Berlichj, S. Bethke”, 0. Biebel n, V. Blobel h, I.J. Bloodwortha, J.E. Bloomer a, P. Bock k, H.M. Bosch k, M. Boutemeur’,

B.T. Bouwense, S. Braibant e, R.M. Brown t, H.J. Burckhart h, C. Burgard=, R. Btirginj, P. Capiluppi b, R.K. Carnegie f, A.A. Carter m, J.R. Carter e, C.Y. Chang 4, C. Charlesworth f,

D.G. Charltona,2, D. Chrisman d, S.L. Chud, P.E.L. Clarke O, I. CohenW, J.E. Conboy O, O.C. Cooker’, M. Cuffiamb, S. Dada”, C. Dallapiccolaq, G.M. Dallavalleb, S. De Jong e,

L.A. de1 Pozo h, K. Desch c, M.S. Dixits, E. do Couto e Silva’, M. Doucet r, E. Duchovni z, G. Duckeckh, I.P. Duerdothp, J.E.G. Edwardsi’, PG. Estabrooksf, H.G. Evans’,

M. Evans m, F. Fabbri b, P. Fath k, F. Fiedlere, M. Fierro b, H.M. Fischer c, R. Folman ‘, D.G. Fong 4, M. Foucher q, H. Fukui x, A. Ftirtjes h, P. Gagnon g, A. Gaidot ‘, J.W. Gary d,

J. Gascon’, S.M. Gascon-Shotkinq, N.I. Geddesf, C. Geich-GimbelC, F.X. Gentit ‘, T. Geralis t, G. Giacomelli b, P. Giacomelli d, R. Giacomelli b, V. Gibsone, W.R. Gibson”,

D.M. Gingrich adT1, J. Goldberg v, M.J. Goodricke, W. Gorn d, C. Grandi b, E. Gross z, M. GruwC h, C. Hajdu af, G.G. Hanson e, M. Hansroul h, M. Hapke m, C.K. Hargrove s,

PA. Hart i, C. Hartmann”, M. Hauschild h, C.M. Hawkes e, R. Hawkings h, R.J. Hemingway f, G. Hertenj, R.D. Heuer h, M.D. Hildrethh, J.C. Hill e, S.J. Hillier a,

T. Hilsej, J. Hoare e, P.R. Hobson Y, R.J. Homer a, A.K. HonmaabT1, D. Horvath af%3, R. Howard ac, R.E. Hughes-Jones P, D.E. Hutchcroft e, P. Igo-Kemenes k, D.C. Imrie Y,

M.R. Ingrami’, A. Jawahery 9, P.W. Jeffreys t, H. Jeremie’, M. Jimack a, A. Joly r, C.R. Jones e, G. Jones P, M. Jones f, R.W.L. Jones h, U. Jost k, P. Jovanovic ‘, T.R. Junk h,

D. Karlen f, K. Kawagoe”, T. KawamotoX, R.K. Keeler , ab R.G. Kelloggq, B.W. Kennedy t, B.J. King h, J. Kirk ac, S. Kluth h, T. Kobayashi x, M. j, D.S. Koetke f, T.P. Kokott ‘,

S. Komamiya”, R. Kowalewski h, T. Kress k, P Krieger f, J. von Krogh k, P. Kyberd m, G.D. Lafferty P, H. Lafoux”, R. Lahmann 9, W.P. Lai ‘, D. Lanske n, J. Lauber O,

S.R. Lautenschlager ae, J.G. Layter d, D. Lazic “, A.M. Lee %, E. Lefebvre r, D. Lellouch ‘,

0370-2693/96/$12.00 Copyright 0 1996 Elsevier Science B.V. All rights reserved. PZI SO370-2693(96)00860-X

378 OPAL Collaboration/Physics Letters B 384 (1996) 377-387

J. Letts b, L. Levinson”, C. Lewis’, S.L. Lloydm, F.K. LoebingerP, G.D. Longq, M.J. Losty s, J. Ludwig j, A. Luigj, A. MalikU, M. Mannelli h, S. Marcellini b, C. Markus ‘,

A.J. Martin m, J.P. Martin r, G. Martinez q, T. Mashimo ‘, W. Matthews Y, P. Mattig ‘, W.J. McDonald ad, J. McKenna ac, E.A. Mckigney O, T.J. McMahon a, AI. McNab m,

R.A. McPherson h, F. Meijers h, S. Menke ‘, ES. Merritt i, H. Mes g, J. Meyer aa, A. Michelini b, G. Mikenberg ‘, D.J. Miller O, R. Mir ‘, W. Mohr j, A. Montanari b, T. Mori ‘, M. Morii x, U. Mtiller ‘, H.A. Neal h, B. Nellen c, B. Nijjhar p, R. Nisius h, S.W. O’Neale a,

F.G. Oakham s, F. Odorici b, H.O. Ogren ‘, T. Omori ‘, M.J. Oreglia i, S. Orito ‘, J. Palinkasas34, J.P. Pansart ‘, G. Pasztor &, J.R. Paterp, G.N. Patrickf, M.J. Pearcea,

S. Petzold aa, P. Pfeifenschneider n, J.E. Pilcher i, J. Pinfoldad, D.E. Plane h, P. Poffenberger ab, B. Poli b, A. Posthaus ‘, H. Przysiezniakad, D.L. Rees a, D. Rigby a,

S.A. Robins m, N. Rodning ad, J.M. Roney ab, A. Rooke O, E. Ros h, A.M. Rossi b, M. Rosvickab, P. Routenburg ad, Y. Rozen ‘, K. Rungej, 0. Runolfsson h, U. Ruppel n, D.R. Rust!, R. Rylkoy, E.K.G. Sarkisyanw, M. SasakiX, C. Sbarrab, A.D. Schailehy5,

0. Schailej, F. Scharf c, P. Scharff-Hansenh, P. Schenkd, B. Schmitt c, S. Schmittk, M. Schr6derh, H.C. Schultz-Coulonj, M. Schulzh, P. SchiitzC, W.G. Scottt, T.G. Shearsr,

B.C. Shend, C.H. Shepherd-Themistocleousaa, P. Sherwood’, G.P. Siroli b, A. Sittler”, A. Skillman’, A. Skuja 9, A.M. Smithh, T.J. Smithab, G.A. Snowq, R. Sobie ab,

S. Siildner-Remboldj, R.W. Springer ad, M. Sproston t, A. Stahl ‘, M. Starksl, M. Steiert k, K. Stephensr, J. Steuerer aa, B. StockhausenC, D. StromS, F. Strumiah, P. Szymanskit,

R. Tafirout r, S.D. Talbot ‘, S. Tanaka ‘, P. Taras r, S. Tarem”, M. Tecchio h, M. Thiergenj, M.A. Thomson h, E. von Tijrne ‘, S. Towers f, M. Tscheulinj, T. Tsukamoto ‘, E. TsurW,

A.S. Turcot’, M.F. Turner-Watson h, P. Utzatk, R. Van Kooten”, G. Vasseur u, M. Verzocchij, P. Vikas’, M. Vincter ab, E.H. Vokurkar, F. Wackerlej, A. Wagneraa, C.P. Ward e, D.R. Ward e, J.J. Ward O, P.M. Watkins a, A.T. Watson a, N.K. Watsons,

P. Weber f, P.S. Wells h, N. Wermes ‘, J.S. White ab, B. Wilkensi, G.W. Wilson aa, J.A. Wilson a, T. Wlodek”, G. Wolf ‘, S. Wottone, T.R. Wyatt P, S. Yamashita”,

G. Yekutieli ‘, V. Zacek r a School of Physics and Space Research, University of Birmingham, Birmingham B15 2T1: UK

b Dipartimento di Fisica dell’ Vniversita di Bologna and INFN, I-40126 Bologna, Italy c Physikalisches Institut, Vniversitiit Bonn, D-53115 Bonn, Germany

d Department of Physics, University of Caltfornia, Riverside CA 92521, USA e Cavendish Laboratory, Cambridge CB3 OHE, UK

f Ottawa-Carleton Institute for Physics, Depurtment of Physics, Carleton University, Ottawa, Ontario KIS 5B6, Canada g Centre for Research in Particle Physics, Carleton University, Ottawa, Ontario KIS 5B6, Canada

h CERN, European Organisation for Particle Physics, CH-1211 Geneva 23, Switzerland i Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago IL 60637, USA

j Fakultatfilr Physik, Albert Ludwigs Vniversitiit, D-79104 Freiburg, Germany k Physikalisches Institut, Vniversitiit Heidelberg, D-69120 Heidelberg, Germany

’ Indiana University, Department of Physics, Swain Hall West 117, Bloomington IN 47405, USA m Queen Mary and Westfield College, University of London, London El 4NS, UK

n Technische Hochschule Aachen, III Physikalisches Institut, Sommerjieldstrasse 26-28, D-52056 Aachen, Germany a University College London, London WClE 6BT UK

P Department of Physics, Schuster Laboratory, The University, Manchester Ml3 9PL, UK 9 Department of Physics, University of Maryland, College Park, MD 20742, USA


’ Laboratoire de Physique Nucl&aire, Vniversite’ de Mont&al, Montrkal, Quebec H3C 3J7, Canada ’ University of Oregon, Department of Physics, Eugene OR 97403, USA

’ Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 OQX, UK ’ CEA, DAPNIMSPP, CE-Saclay, F-91 191 Gif-sur-Yvette, France

’ Department of Physics, Technion-lsrael Institute of Technology, Haifa 32000, Israel w Department of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel

’ International Centre for Elementary Particle Physics and Department of Physics, University of Tokyo, Tokyo 113, Japan and Kobe University, Kobe 657, Japan

Y Brunei Universiiy, Vxbridge, Middlesex VB8 3PH, UK ’ Particle Physics Department, Weizmann Institute of Science, Rehovot 76100, Israel

aa Universitiit Hamburg/lDESI: II Institut fiir Experimental Physik, Notkestrasse 85, D-22607 Hamburg, Germany ab Universie of Victoria, Department of Physics, P 0 Box 3055, Victoria BC VSW 3P6, Canada

ac University of British Columbia, Department of Physics, Vancouver BC V6T 121, Canada ad University of Alberta, Department of Physics, Edmonton AB T6G 2J1, Canada

ae Duke University, Department of Physics, Durham, NC 27708-0305, USA af Research Institute for Pariicle and Nuclear Physics, H-1.525 Budapest, PO Box 49, Hungary

ag Institute of Nuclear Research, H-4001 Debrecen, PO Box 51, Hungary

Received 23 May 1996 Editor: K. Winter

Abstract

The spin composition of Al?, AA and I%& pairs at low invariant mass values has been measured for the first time in mnltihadronic Z” &cays with the OPAL detector at LEP. No single spin state has been observed in the A& sample, verifying that the low mass enhancement in this sample, attributed to local baryon number compensation, is not a resonance state. The fraction of the spin 1 contribution to the Al? pairs was found to be consistent with the value 0.75, as expected from a statistical spin mixture. This may be the net effect of many different QCD processes which contribute to the hyperon anti-hyperon pair production. The spin composition of the identical AA and &A pairs, well above threshold, is found to be similar to that of the Ai sample. A AA emitter dimension is estimated from the data assuming the onset of the Pauli exclusion principle near threshold.

1. Introduction

The fragmentation and hadronisation processes in

high energy particle interactions have been the subject

of many QCD-based theoretical investigations [ 11. These theoretical models predict general features of

multihadron states, such as the jet structure and the inclusive particle momentum spectrum, which have been confronted with the experimental findings. Addi- tional information concerning the hadronisation processes comes from correlation studies of pairs of par-

1 And at TRIUMF, Vancouver, Canada V6T 2A3 2 And Royal Society University Research Fellow

3 And Institute of Nuclear Research, Debrecen, Hungary 4 And Department of Experimental Physics, Lajos Kossuth Uni-

versity, Debrecen, Hungary 5 And Ludwig-Maximilians-UniversiW, Miinchen, Germany

titles. Among these are the study of the Bose-Einstein Correlations (BEC) of identical bosons, mainly identical pions. From these studies one is able to extract the dimension of the particle emitter. Recently a new

approach to the description of the parton to hadron conversion has been proposed [ 21, which is applied to

final state bosons. In this approach the BEC of identical pions form an integral part of the model so that the BEC experimental measurements can serve to extract the basic model parameters. The BEC have also been investigated in the framework of the Lund fragmentation model [ 31 and compared to experimental data.

When extending such models to include baryons in the final state, the BEC obviously are no longer appli- cable and other correlations should be considered in order to investigate the underlying baryon production processes. Among those of interest is the spin com-


position of the baryon anti-baryon (BB) final states produced in the hadronisation process. For two spin

l/2 baryons the total spin, S = Sg + Sg, may be 0 or 1. Baryon anti-baryon pairs can be produced by several QCD processes in high energy reactions. If the BB pair

production is for example dominated by a single gluon emission, in analogy to the ‘colour octet’ mechanism

[4] which is applied to J/(cl and Y production, then the S = 1 state may dominate over the S = 0 state due

to the vector (J ’ = l-) nature of the gluon. This will

be the case only as long as the soft gluons, which are needed to balance the colour, do not disturb too much the quantum state of the di-baryon system. If however

many other diagrams, like those involving several gluons or the so called ‘popcorn’ IS] mechanism, also contribute to BB pair production, then one may have

a statistical-like spin composition where, due to the 2S+l factor, the S = 1 fraction is three times larger than that of the S = 0.

The main interest in studying the spin composition of identical baryons as a function of their invariant

mass stem from the possibility to observe the decrease of the S = 1 state contribution, due to the Pauli exclusion principle, as the di-baryon energy approaches

threshold. This then can serve as a measure of the baryon emitter dimension [6] in analogy to that

obtained from the BEC measurements of identical bosons.

Here we describe a spin correlation analysis of inclusive A& Ah and AA pairs which is only depen- dent on the relative polarisation of the two hyperons. The analysis is based on multihadronic 2’ decay data recorded by the OPAL detector during the years 1990 to 1994 corresponding to an integrated luminosity of 137 pb-’ . We estimate that in our event sample about 20% of the h’s originate from weak decays of baryons, mainly B hyperons [ 71, and the rest stems from strong interactions. In addition we have used in the analysis 7.1 x lo6 JETSET7.3 and JETSET7.4 Monte Carlo [ 81 events with a full detector simulation [9]. The JETSET parameters were adapted to OPAL data [ lo]. These Monte Carlo samples do not include any spin effects in the A production and decay. The data are stud- ied as a function of the variable Q, frequently used in the BEC studies of identical bosons, which is related to the di-A invariant mass, MAA, through the expression

Q = dq and is equal to zero at threshold.

In Section 2 we outline the method used for the spin composition measurement and in Section 3 we

describe the procedure adopted to obtain the experi-

mental data samples and evaluate their backgrounds. In Section 4 our results for the spin compositions are

described, and finally in Section 5 a summary and conclusions are given.

2. The method

In general it is very difficult to measure in high energy reactions the relative contributions of the S = 0 and the S = 1 states to a di-baryon (BiB2 or Bi&) system such as a pp pair. However, a relatively simple

experimental method has recently been proposed [ 61 for the measurement of the S = 0 and S = 1 contribu-

tions to a given system of two spin 1 I2 weakly decay-

ing hyperons, like AA and AA pairs, which is independent of their relative angular momentum e. A com- prehensive description of this method can be found in Ref. [ 61, so here we will only outline in brief some

of the aspects which are relevant to our analysis. The spin composition measurement is based on the

distribution dN/dy*, in the di-hyperon cents-e of mass

(CM) system, where y* is the cosine of the angle between the two hyperons’ decay protons, each measured in its parent hyperon rest frame (see Section 4 for further details). If LzB is the hyperon decay parameter arising from parity violation, then the decay angular distribution of each hyperon in its rest frame isoftheform [ll]

dA’,‘d cos 6, = 1 - CY~ - cos 6,

where f3, is the angle of the proton direction relative to the polarisation axis of the hyperon. The Wigner- Eckart theorem [ 121 then gives a relation between the average value of y* and the average cos 0, values:

(Y”) {

-3 for S = 0

(cos~pl)(cos~pz) = -l-l forS = 1

where S is the spin state of the di-baryon system. For the case of interest here, (y*) can be calculated at the AA threshold by using the well measured czA value [ 131 of 0.642 f 0.013. Due to the fact that the A is a spin l/2 particle, the dN/dy* distribution cannot have a y* dependence higher than its first power, so that the

OPAL Collaboration/ Physics Letters B 384 (1996) 377-387 381

average value (y*) uniquely determines the angular distribution. Using a;\ and the fact that CX~ = -an, one is then able to derive the y* angular distributions

at the di-hyperon threshold energy 6 . Thus for the S = 0 and S = 1 A& states one gets

dN/dy*Js=o = 1+ a$ * y*,

dN/dy*ls,t = 1 - +a; . y* (1)

whereas for the S = 0 and S = 1 AA and I?n identical hyperon states one obtains

dN,‘dy* Isa = 1 - CY; . y*,

dN/dy*Is=, = 1 + $a; . y* (2)

It should be noted that for e = 0, the S = 1 state of

two identical spin l/2 particles is forbidden by the

Pauli exclusion principle. Even though these dN/dy*

distributions are derived for a di-hyperon system at threshold, they can still be used at higher, but not

relativistic, di-hyperon CM energies provided that the

nucleon decay products are transformed to their parent hyperon rest frame (see Ref. [ 61) . Therefore we have limited our analysis to Q values less than 2.5 GeV.

Using the above equations one can evaluate, for a given di-A data sample, the relative contributions of the S = 0 and S = 1 states by fitting the expression:

dN/dy* = (1 -E) .dN/dy*Is=o+E.dN/dy*Is=1 (3)

to the measured dN/dy* distribution. The parameter E is the fraction of the S = 1 state contribution to the di-hyperon system. For a statistical spin mixture en- semble, where each spin state probability is weighted by the factor 2S+l, E is equal to 0.75 which corre-

sponds to a constant dN/dy* distribution.

3. Experimental setup and data selection

3.1. The OPAL detector

Details of the OPAL detector and its performance at the LEP e+e- collider are given elsewhere [ 141. Here we will describe briefly only those detector com- ponents pertinent to the present analysis, namely the central tracking chambers.

6 Note that at threshold the single hyperon CM system, where

(cos S,) is evaluated, is the same as that of the di-hyperon system.

The central tracking chambers consist of a preci- sion vertex detector, a large jet chamber, and addi-

tional z-chambers surrounding the jet chamber. The vertex detector is a 1 m long, two-layer cylindrical drift chamber which surrounds the beam pipe7 . The jet chamber has a length of 4 m and a diameter of 3.7 m. It is divided into 24 sectors in 4, each equipped

with 159 sense wires parallel to the beam ensuring

a large number of measured points even for particles emerging from a secondary vertex. The jet chamber also provides a measurement of the specific energy

loss, dE/dx, of charged particles [ 151. A resolution of 34% on dE/dx has been obtained, allowing particle identification over a large momentum range. The

z-chambers, 4 m long, 50 cm wide and 59 mm thick, allow a precise measurement of the z-coordinate of the charged tracks. They cover polar angles from 44” to 136” and 94% of the azimuthal angular range. All the

chambers are contained in a solenoid providing an ax- ial magnetic field of 0.435 T. The combination of these chambers leads to a momentum resolution of ap,lpr

M J(0.02)2 -t (0.0015 a~[)~, where pr in GeV/c is the transverse momentum with respect to the beam direction. The first term under the square root sign represents the contribution from multiple scattering [ 161.

3.2. Data selection

Hadronic Z” decays were selected according to the

number of charged tracks and the visible energy of the event, using the criteria described in Ref. [ 171. In addition, events where the thrust axis lay close to the

beam axis were rejected by requiring 1 cos i?hrust( < 0.9, where 8arust is the polar angle of the thrust vector determined from charged tracks. The analysis was per-

formed on data collected on and around the Z” peak. with the requirement that the jet and z-chambers were fully operational, a total of 3.3 x lo6 Z” hadronic decay events satisfied these selection criteria. The A baryons were selected by reconstructing the decay A --+ prr, applying an improved version of the selection described as method 1 in Ref. [ 71. All pairs of tracks with opposite charge were examined and the higher

7 A right-handed coordinate system is adopted by OPAL, where

the n-axis points to the centre of the LEP ring, and positive z is along the electron beam direction. The angles 0 and 4 are the

bolar and azimuthal angles, respectively.

382 OPAL Collaborarion/Physics Letters B 384 (1996) 377-387

momentum track was assigned to be the proton track. In addition, the measurement of dE/dx were required to be consistent with the p and n- hypotheses. Inter-

section points of track pairs in the plane perpendicu-

lar to the beam axis were considered to be secondary vertex candidates if the following requirements were

satisfied: the radial distance from the intersection point to the primary vertex had to be larger than 1 cm and smaller than 150 cm; the reconstructed momentum vector of the A can- didate in the plane perpendicular to the beam axis had to point within 2” to the primary vertex; if the secondary vertex was reconstructed inside the

jet chamber volume, the radius of the first jet chamber hit of each of the two tracks had to be less than

3 cm from the secondary vertex; if the secondary vertex was not reconstructed inside the jet chamber, the impact parameter transverse to the beam direction (do) of the pion with respect to

the main vertex had to be larger than 3 mm and the do of the proton track had to exceed 1 mm; photon conversions were rejected if the invariant mass of the track pair, assumed to be an efe- pair, was smaller than 40 MeV,

a mass window cut of & 6 MeV, around our mean fitted A mass value of 1115.7 MeV, was applied.

This corresponds to & 2.5 times our A mass resolution.

In this way a total of 7336 A pairs were selected after verifying that they do not have a track in com- mon. These were grouped into the three di-hyperon samples given in Table 1. The corresponding numbers of Monte Carlo A pairs that passed our selection criteria are also shown. Good agreement is seen between the composition of the Monte Carlo generated sample and the data.

Due to the fact that the initial e’e- system is an eigenstate of the charge conjugation operator, the inclusive properties of the Ah and the &A samples should be identical. Experimentally this is not exactly the case since the A and ;i and their decay products have different reaction cross sections with the LEP beam pipe and the OPAL detector materials. In fact, the number of selected AA pairs is smaller by about 11% than that of the AA pairs. In every step of the analysis, where for physics reasons we added these two samples together, we first ascertained that apart

Table 1 The total number of data and Monte Carlo selected A pairs.

Data Monte Carlo

Sample No. of pairs Fraction No. of pairs Fraction

AK 5255 71.6% 9628 71.9% Ah 1095 15.0% 2037 15.2% iiii 986 13.4% 1735 12.9% (Ah + Kli) (2081) (28.4%) (3771) (28.1%)

Total 7336 100% 13399 100%

Fig. 1. The invariant mass and Q distributions of the Ai and the combined AA + ilil data samples.

from the obvious reduction in the number of ii pairs, the two samples behaved similarly.

In Fig. la the measured invariant mass distributions of the A& and the combined AA and xl? sample are shown. In the AA distribution a broad low mass en-

hancement is seen, which in various fragmentation models is associated with local baryon number con- servation [ 1,8] . No other significant resonance signal is seen * in the mass range from 4 to 12 GeV.

The distributions of the Ai and the combined AA and hi samples are shown in Fig. lb as a function of the Q variable used in our analysis. As can be seen, above Q = 4 GeV the two distributions essentially co- incide, whereas below 4 GeV the AA distribution rises due to the correlated production in the hadronisation process.

To exclude from the analysis A’s that contain a primary s-quark from Z” --f sS decays, we required that the relative energy XE s En/Ebea,,, was less than 0.3 following Ref. [ 181. This amounted to about 2% of our data, too small for a meaningful spin correlation

* We estimate that from the decay chain Zo -+ J/fix; J/lc, + AA at most five events should contribute to our Al? sample.

OPAL Collaboration/Physics Letters B 384 (1996) 377-387 383

0.8

0.6

Fig. 2. The background fraction, fan, plotted as a function of Q for the di-A samples as obtained from the OPAL. measured data (points with error bars) and from the Monte Carlo studies (lined histograms). The AA (id) data below Q = 0.5 GeV is not used in the analysis. The error bars represent the statistical and systematic errors added in quadrature.

analysis.

3.3. Background

The fraction of background (fno) in our samples was estimated from the data. We considered the two-dimensional data invariant mass distribution of M(ptni) versus M(pz?rz). Combinations in which both M(pt~t ) and M(p2~2) fell inside the f 6 MeV A signal region were the pairs used in our spin compo-

sition analysis. The background was then determined by the pairs which fell outside the signal region, as described in Ref. [7]. As a check the background was also investigated with the JETSET Monte Carlo

generated sample. The fraction fno and its dependence on Q, as ob-

tained from the data and the Monte Carlo, are shown in Fig. 2 for the Ai and for the combined AA and &i samples. The purity of the A& sample below Q = 2.5 GeV is constant within errors, having a value of about 90%. This is not the case for the identical hyperon pair samples, where the purity decreases as Q decreases, reaching a level of only about 35% at low Q values. The low statistics at Q < 0.5 GeV, together with the low purity of the sample, do not allow a significant measurement of the spin composition of the identical hyperons at this low Q region.

4. Spin composition measurements

To measure the spin composition according to the method outlined in Section 2, we performed two Lorentz transformations on each hyperon pair and its

decay protons: (i) a transformation from the laboratory system to

the di-hyperon CM system, followed by

(ii) a transformation of each proton momentum to its parent hyperon rest frame.

After these transformations, y*, the cosine of the angle

between the momentum vectors of the decay protons, was calculated. The resolution of y* is about 0.05, as

determined from Monte Carlo studies. In order to ac-

count for background effects in our spin composition

measurements, we initially modified Eq. (3) to read

dN/dy* = ( 1 - fBG) . { (1 - E) . dN/dy* Isa

+E.dN/dy*ls=1}+fsc.(l+S.y*> (4)

where the background fraction fao is allowed to have a linear y* dependence with a slope 8. In a systematic study of the background derived from the OPAL data and the Monte Carlo samples, no deviations from a constant y* behaviour were found over the whole an-

gular range so that the slope parameter S could be set to zero, Thus Eq. (4) was simplified to:

dN/dy* = ( 1 - fno) . { ( 1 - E) . dN/dy* Is*

+E -dN/dy*Is=~} + ~BG (5)

For the spin analysis we have divided the data into five Q regions within the range of 0.2 to 2.5 GeV as specified in Table 2.

To obtain the value of E we have fitted Eq. (5), in each Q range, event by event using the maximum likelihood method. The experimental dN/dy* distri-

butions are shown in Fig. 3 together with the fitted angular distributions. The E values obtained from the fits and their errors, together with the number of data pairs and their background fractions, are presented in Table 2 for the five chosen Q intervals. The dominant sources of systematic errors are the uncertainties of the background levels and the slope of their y* distributions. To evaluate these we have repeated the procedure described in Section 3.3 varying the position of the areas outside the di-A signal region which were used to estimate fBG. The systematic error due to the

384

Table 2

OPAL Collaboration/Physics Letters B 384 (1996) 377-387

Final results for the fraction of the S = 1 contribution to the Ai pairs sample and to the combined Ah and I%A sample in five Q regions as obtained from the maximum likelihood fits of the parameter E. Fit results are also shown for the entire Q range. The statistical errors are those given by the fits.

Q range (GeV)

0.2-0.5 0.5-1.0 1.0-1.5 1.5-2.0 2.0-2.5 0.2-2.5 (Q) (Gev) 0.39 0.76 1.24 1.73 2.23 1.29

Ax data sample No. of pairs 223 894 928 591 452 3088 ~BG (%I 9.1 11.1 9.8 10.7 10.7 10.4

E 0.81 0.69 0.77 0.63 0.67 0.71 he (stat) 0.21 0.12 0.11 0.14 0.16 0.06 be (syst) 0.03 0.04 0.03 0.04 0.04 0.03

Q range (GeV)

0.2-0.5 0.5-1.0 1.0-1.5 1.5-2.0 2.0-2.5 0.5-2.5 (Q) (GeV) - 0.77 1.25 1.72 2.24 1.53

Combined Ah and Ali data sample No. of pairs 99 131 124 123 477 ~BG (%I 65.7 58.0 39.8 25.6 46.2

E -0.59 0.88 0.72 0.93 0.67 AE (stat) 0.90 0.62 0.46 0.36 0.26 AE (syst) 0.48 0.11 0.05 0.04 0.10

Table 3 The E systematic uncertainties and their sources. These are added in quadrature to obtain At- (syst), the overall systematic error,

Source Q range (GeV)

0.2-0.5 0.5-1.0 1.0-1.5 1.5-2.0 2.0-2.5 0.2-2.5

Ai data sample fBG 0.002 0.001 0.001 0.002 0.002 0.001 slope 6 0.034 0.035 0.034 0.034 0.034 0.034

alI 0.003 0.003 0.001 0.005 0.004 0.002

AE (syst) 0.034 0.035 0.034 0.035 0.035 0.034

Source Q range (GeV)

0.2-0.5 0.5-1.0 1.0-1.5 1.5-2.0 2.0-2.5 0.5-2.5

Combined AA and 1?i data sample fBG 0.448 0.027 0.003 0.016 0.018 slope 6 0.173 0.102 0.052 0.041 0.103 LyA 0.056 0.006 0.001 0.008 0.006

AE (syst) _ 0.483 0.106 0.052 0.045 0.104

uncertainties of the 6 slope value were estimated by varying the 6 values by &AS given by the fits to the Monte Carlo y* distributions. We checked that our spin composition results are stable, within the statistical er-

rors, when the mass window cut applied to the M( pz-) distribution was varied between f 5 to f 10 MeV and so verified that this contribution to the systematic errors was negligible. Finally we have included in the

OPAL Colluboration/ Physics Letters B 3&f (1996) 377-387 385

systematic error the uncertainty on the world average value of cry used in Eqs. ( 1) and (2). The individ- ual contributions to the systematic error on E and their sum in quadrature, AE (syst), are given in Table 3.

In Fig. 4 we present our final results for the spin

composition as a function of Q, with E representing the relative contribution of the S = 1 state. The full circles

are the results for the AA sample and the open circles

are for the combined AR and AA sample. The error

bars represent the statistical errors added in quadrature with the systematic uncertainties. In the Q range of 1 .O to 2.5 GeV the spin composition of both samples is consistent with the value of E = 0.75 which is also the value expected for a statistical spin mixture. In the low

Q region of less than 1 .O GeV, the spin composition of

the AA remains the same as at higher Q values, namely E x 0.75 whereas the E value of the identical hyperon pair sample is seen to decrease but is still consistent

within its error with a statistical spin mixture. If at low Q values the s-wave (j = 0) is dominant

due to the angular momentum barrier, the E of the combined Ah and AA sample should approach zero due to the Pauli exclusion principle. This may allow the emitter dimension of the identical AA (AA) pairs to be extracted. To this end we assume that at high

Q values E approaches, from below, the value of 0.75 as expected for a statistical spin mixture, This value is also consistent within errors with our experimental findings. To describe the rise of the S = 0 contribution,

given here by 1 - E, as Q approaches zero, we have adopted the Goldhaber parametrisation [ 191 which describes the Bose-Einstein correlation enhancement.

Thus the function to be fitted is the one given in Eq. (5) with a Q dependence of E given by:

E(Q) = 0.75. (1 - KQ”R’,,) (6)

Here Rnn, the free parameter to be fitted, may be taken as a measure of the size of the identical di- baryon emitter region in analogy to its role in the BEC studies. In this way one is able to carry out a fit over the whole Q range from 0.5 to 2.5 GeV avoiding the need for binning. An unbinned maximum likelihood fit of RAa to the data has been performed, with the result of RAA = 0.19 2t.z; fm, where the errors are taken from the fit. The systematic error is at the level of 0.02 fm. However, Rhh is consistent with infinity at the level of 1.2 standard deviations9 . Expressing this

OPAL __

0 ::::):x:)::::/::::

150 l.O<Q<lS GeV

Fig. 3. The measured y* distributions obtained from the Ai and

from the combined Ah and hi data samples. The dashed lines

represent the results of an unbinned maximum likelihood fit (see

Table 2).

measurement as a limit, we deduce that R*A > 0.11 fm at the 90% confidence level. The result of the fit is shown in Fig. 4 by the dashed line.

5. Summary and conclusions

A first measurement of the spin composition of AA, AA and AA pairs in high energy reactions has been

carried out in the fragmentation region of the Za multihadron decays. We have used a recently proposed method which is independent of the relative di-A angular momentum. Since this method is only valid as long as the energies of the A’s are non-relativistic in their overall CM system, the analysis was restricted to the region of Q 5 2.5 GeV The lower Q limits used in our spin analysis were dictated by the statistics and purity of the samples. These limits were set to 0.2 GeV for the AA sample and to 0.5 GeV for the AA and AA data. In our spin analysis, which is model

g More than one standard deviation above the fitted Rnn value the likelihood function does not follow a Gaussian distribution but

reaches a plateau.


2- l &i OPAL - &

-0.5

-1 : I

0 0.5 1 1.5 2

Q [Ge:;’

Fig. 4. The measured fraction E of the S = 1 state contributions to the di-A systems as a function of Q. The full circles are for the Ad sample, and the open circles are for the combined Ah and xl? sample. The error bars represent the statistical and systematic errors added in quadrature. The E = 0.75 dot-dashed line represents the statistical spin distribution. The dashed line describes the Pauli exclusion effect for an emitter radius of 0.19 fm obtained in an unbinned maximum likelihood fit to the combined AA and i?A sample (see text).

independent, we have used as much as possible the

OPAL data to evaluate the purity of our samples and the effects of the background on our measurements.

Over the entire Q range analysed, no significant contribution from resonance decays into a AA pair is seen, although there is a broad threshold enhancement in the region of 0.5 < Q < 1.5 GeV. In various fragmentation models this enhancement is accounted for by assuming Iocal baryon number compensation. This interpretation is supported by our spin measurement in this enhancement region for which we obtain E = 0.73 & 0.08 f 0.04, indicating that the S = 0 and the S = 1 states contribute with a relative strength propor- tional to 2s + 1.

No evidence for exotic di-baryon resonances is seen in our combined Ah and AA mass distribution above Q = 1 .O GeV. The errors of our spin measurements are too large to detect any region which is clearly a single spin state. The Q region below 0.5 GeV, where the Ah resonance state referred to as the H particle [20] is most likely to be present, is inaccessible to us due to insufficient statistics and low A purity. In the Q region between 0.5 and 1.0 GeV, the S = 1 contribution is found to be consistent with zero, associated however

with a large error so that a statistical mixture cannot be excluded. If this behaviour is attributed to the Pauli

exclusion principle, then it is best fitted by an emitter radius of 0.19 fm with an asymmetric error leading to

a limit of RAA > 0.11 fm at 90% confidence level. Apart from this single low E value, the spin com-

position over the whole analysed Q region, of both the A& and the identical hyperon pairs AA and 1?1? is

consistent with the S = 1 state having a contribution of about 75%. Summing up all the Al? data one obtains the value E = 0.71 f 0.06 f 0.03 which is more than 4 standard deviations away from a pure S = 1 state. For the identical hyperons the corresponding re-

sult averaged over the 0.5 < Q < 2.5 GeV range is E = 0.67 f 0.26 +O.lO.

If the properties of Al? pairs produced in Z” decays are dominated by the vector nature of a single gluon, the state S*i = 1 should predominate and yield E M 1.

Due to the fact that an isolated gluon cannot produce a colourless A& pair, a reduction in the contribution

of the S = 1 state can occur during the colour fading process mediated by soft gluon emission. Thus in the absence of reliable QCD calculations, a value of E =

0.75 from this process cannot yet be ruled out. How- ever, the observation that E for the Ai pairs is con-

sistent with the value 0.75 over the whole analysed Q range, as also for the identical A hyperons at Q above

1 .O GeV, strongly suggests that the spin compositions of all di-A samples are as expected from a statistical spin distribution, representing an average over many allowed QCD production processes and baryons’ decay.

Acknowledgements

We thank J. Ellis, K. Kinder-Geiger and H.J. Lipkin for many helpful discussions concerning the theoretical aspects of this work. It is a pleasure to thank the SL Division for their efficient operation of the LEP accelerator and for their continuing close cooperation with our experimental group. In addition to the sup- port staff at our own institutions we are pleased to acknowledge the Department of Energy, USA, National Science Foundation, USA, Particle Physics and Astronomy Research Council,

UK

OPAL Collaboration/Physics Letters B 384 (1996) 377-387 387

Natural Sciences and Engineering Research Council, [ 51 B. Andersson, G. Gustafson and T. Sjostrand, Physica Scripta

Canada, 32 (1985) 574.

Israel Ministry of Science, Israel Science Foundation, administered by the Israel Academy of Science and Humanities, Minerva Gesellschaft,

[6] G. Alexander and H.J. Lipkin, Phys. Lett. B 352 (1995) 162. [7] OPAL Collab., P Acton et al., Phys. Lett. B 291 (1992) 503.

[81

Japanese Ministry of Education, Science and Culture (the Monbusho) and a grant under the Monbusho International Science Research Program, German Israeli Bi-national Science Foundation

(GIF), Direction des Sciences de la Matike du Commissariat a 1’Energie Atomique, France, Bundesministerium fti Bildung, Wissenschaft, Forschung und Technologie, Germany, National Research Council of Canada, Hungarian Foundation for Scientific Research, OTKA T-016660, and OTKA F-015089.

[91 [lOI

T. Sjiistrand, Comp. Phys. Con& 39 (1986) 347; Comp. Phys. Comm. 82 (1994) 74; T. Sjiistrand and M. Bengtsson, Comp. Phys. Comm. 43 (1987) 367. J. Allison et al., Nucl. Instr. Meth. A 317 (1992) 47. OPAL Collab., P. Acton et al., Z. Phys. C 58 (1993) 387; OPAL Collab., G. Alexander et al., Z. Phys. C 69 (1996) 543.

[111

El21

[131

1141

See for example E. Segre, Nuclei and Particles, 2nd Edition (Benjamin/Cummings Publishing Co.), p. 876. E.P. Wigner, Z. Phys. 43 (1927) 624; C. Eckart, Rev. Mod. Phys. 2 (1930) 305. L. Montanet et al., Review of Particle Properties, Phys. Rev. D 50 part I (1994) 1173. OPAL Collab., K. Ahmet et al., Nucl. Instr. Meth. A 305 (1991) 275; PP. Allport et al., Nucl. Instr. Meth. A 324 (1993) 34; A 346 (1994) 476. M. Hauschild et al., Nucl. Instr. Meth. A 314 (1992) 74. 0. Biebel et al., Nucl. Instr. Meth. A 323 (1992) 169. OPAL Collab., G. Alexander et al., Z. Phys. C 52 (1991) 175.

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Documents

A first measurement of the ΛΛ and ΛΛ (ΛΛ) spin compositions in hadronic Z0 decays